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Understanding Pythagorean Theorem and Trigonometric Ratios in Right Triangles

Discover the foundational concepts of the Pythagorean Theorem and trigonometric ratios with this comprehensive guide. Learn how to identify the sides of a right triangle (Hypotenuse, Opposite, Adjacent) and apply formulas like c² = a² + b². Understand SOH-CAH-TOA to calculate sine, cosine, and tangent, and when to use each formula effectively. The practical application of these concepts is included, along with examples of solving for x using the quadratic formula and using a clinometer for measurement. Perfect for students seeking clarity in geometry and algebra.

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Understanding Pythagorean Theorem and Trigonometric Ratios in Right Triangles

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  1. Trig – So far we have... July 2011

  2. Pythagoras c2= a2+ b2 where c is the hypotenuse = the longest side

  3. SOH-CAH-TOA

  4. 3D Problems

  5. SOH-CAH-TOA

  6. Pythagorasc2 = a2 + b2 so c = (a2+ b2 )^0.5a2= c2 - b2so a = (c2 - b2 )^0.5 b2= c2 - a2 so b = (c2 - a2 )^0.5

  7. How to label a triangle • H = Hypotenuse, which is always opposite the right angle and always the longest side. It does not move, Pythag: H2 = O2 + A2 • O = opposite which is the side opposite the angle we are interested in. • A = Adjacent which lies between the right angle and the angle we are interested in.

  8. Which formulae do I use? Pythag or SOH-CAH-TOA

  9. Which Formulae ?

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  24. Which Formulae ?

  25. Practical measurementUsing a Clinometer

  26. 3D Problem Solving

  27. Today:Algebra recapsolve for xax2 + bx + c = 0Working on problems in the text book and work book.One group at a time measuring the classroom as per yesterday.

  28. solve for xax2 + bx + c = 0

  29. The Quadratic Formulae Proof

  30. Quad Formula fromhttp://users.rcn.com/mwhitney.massed/quadratic_formula_proof.htmlMs Allan’s Wiki:http://2011maths.wikispaces.com/NCEA+Level+1+Trig

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